What is 17/36 plus 15/21?
17/36 plus 15/21 equals 299/252 (or 1 47/252 as a mixed number) (or 1.186508 in decimal form). Learn the step-by-step solution to add 17/36 and 15/21 using Least Common Denominator and simplification.
Exact Answer
17/36 + 15/21 = 299/252
Simplified Fraction
299/252
Mixed Number
1 47/252
Decimal Value
1.186508
Percentage
118.6508%
Step-by-Step Solution: 17/36 + 15/21
Step 1
Find the Least Common Denominator (LCD)
The denominators 36 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 252 (which is smaller than their product 36 × 21 = 756, keeping the calculation simpler).
LCD(36, 21) = 252
Step 2
Convert to Equivalent Fractions with Common Denominator 252
Multiply the numerator and denominator of 17/36 by 7, and multiply the numerator and denominator of 15/21 by 12 so both fractions share the common base 252.
17 × 7/36 × 7 = 119/252 and 15 × 12/21 × 12 = 180/252
Step 3
Add the Numerators
Now add the numerators (119 + 180 = 299) and keep the common denominator 252 unchanged.
119 + 180/252 = 299/252
Step 4
Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 299 and 252 is 1, confirming that 299/252 cannot be reduced further—it is already in its simplest irreducible form.
299/252
Step 5
Convert Improper Fraction to a Mixed Number
Since the numerator (299) is greater than the denominator (252), divide 299 by 252: it goes in 1 whole time(s) with a remainder of 47, giving the mixed number 1 47/252.
299/252 = 147/252
Step 6
Decimal & Percentage Representation
Dividing the numerator 299 by denominator 252 produces a repeating decimal (approximately 1.186508, or 118.6508%).
299 ÷ 252 = 1.186508 (118.6508%)
Visual Representation
The diagram below illustrates 17/36 plus 15/21 visually:
+
=
Summary & Alternative Representations
| Property / Format | Value |
|---|---|
| Lowest Terms Fraction | 299/252 |
| Mixed Number Form | 1 47/252 |
| Decimal Form | 1.186508 |
| Percentage | 118.6508% |
Was this solution helpful?
Help us improve our free step-by-step tools
Frequently Asked Questions
What is 17/36 plus 15/21 as a fraction?
17/36 + 15/21 in simplest fraction form is 299/252 (or 1 47/252 as a mixed number).
What is 17/36 plus 15/21 as a decimal?
17/36 + 15/21 converted to a decimal is 1.186508.
What is 17/36 plus 15/21 as a percentage?
17/36 + 15/21 expressed as a percentage is 118.6508%.
How do you write 17/36 plus 15/21 as a mixed number?
Because the numerator is greater than the denominator, the improper fraction 299/252 can be written as the mixed number 1 47/252.
Does 17/36 plus 15/21 result in a terminating or repeating decimal?
It results in a repeating decimal (approximately 1.186508...) because the denominator contains prime factors other than 2 and 5.